The Grothendieck-Pietsch domination principle for nonlinear summing integral operators

• Autorzy: Karl Lermer
• Języki publikacji: EN

Abstrakty

EN

We transform the concept of p-summing operators, 1≤ p < ∞, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Σ,X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domination principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S,X)-spaces. For p-summing Hammerstein operators we derive the existence of control measures and p-summing extensions to B(Σ,X)-spaces.

Kategorie tematyczne

• 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytski{\u\i}, Uryson, etc.)
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 2
• Strony: 97-112

Daty

wydano

1998

otrzymano

1995-10-30

poprawiono

1997-12-01

Twórcy

autor

Karl Lermer

• Department of Computer Science, The University of Queensland, Brisbane, Queensland 4072, Australia

Bibliografia

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